1
$\begingroup$

It is common in QED that electron positron pair can scatter into different lepton family such as muon and antimuon pair. Is it possible that two energetic electrons can scatter into two muons ? I have not been able to find any sources treating such a reaction. And I don't see any reason, such as a selection rule, that would prohibit such reaction.

$\endgroup$

2 Answers 2

3
$\begingroup$

No, $ee\to \mu\mu$ is not likely. For charged leptons there is an approximately conserved lepton family number.

It is not strictly conserved, since neutrino mixing may induce violations in it, but it is freakishly small, with a BR bound for $\mu\to e\gamma$ of less than 13 orders of magnitude.

$\endgroup$
2
$\begingroup$

The reaction $$e^-+e^-\to \mu^-+\mu^-$$ is prohibited since it doesn't conserve lepton number. Every family of leptons has a specific lepton number $L_e, L_\mu$ and $L_\tau$. Leptons carry positive lepton number and anti-leptons carry negative lepton number. In the reaction you gave there's $2L_e$ on the left hand side and $2L_\mu$ on the right hand side, and so it's not conserved.

A scattering like $$e^++e^-\to \mu^++\mu^-$$ is not forbidden since on the LHS you have zero lepton number and on the RHS you have zero as well.

$\endgroup$
1
  • 1
    $\begingroup$ Now I see why I couldnt find any source :] Thanks! $\endgroup$
    – user91411
    Aug 26, 2020 at 13:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.